Corrections for seismic data obtained from expanding-spread

ABSTRACT

Seismic signals from detectors forming split spreads are utilized to correct for weathering, elevation, and the like signals from detectors forming an expanded spread. The signals of the seismic section delineated by the expanded spread have applied thereto time changes under the control of a hyperbolic generator. There are generated as a result of the sweeping across the section and lengthwise thereof of the seismic signals the generation of functions utilized to provide normal moveout corrections of greater precision or accuracy than heretofore. With the normal moveout corrections of greater accuracy applied to the signals of the seismic section, additional corrections are made for dip and thereafter for delineation of the velocity characteristics of the earth along the stratigraphic column. There is included provision not only for identification of primary reflections and multiples but also for the elimination of multiples from the signals of the seismic section. The foregoing operations are carried out in an automatic system which may be either of the analog or digital type.

United States Patent Musgrave 1 CORRECTIONS FOR SEISMIC DATA OBTAINED FROM EXPANDING- SPREAD [72] Inventor: Albert W. Musgrave, Dallas, Tex.

[73] Assignee: Mobil Oil Corporation [22] Filed: Dec. 28, 1970 [21] Appl. No.: 101,776

Related US. Application Data [63] Continuation of Ser. No. 496,735, Sept. 30,

1965, abandoned, which is a continuation of Ser. No. 95,1 1 1, March 13, 1961, abandoned.

52 us. or ..340 1s.s TD, 340/155 R, 340/ 15.5 MC, 346/33 (3 51 1m. (:1. ..'.'...'....G0iv 1724 [58] Field of Search.340/l55 TD, 155 MC; 346/33 C OTHER PUBLICATIONS Seismic Velocities from Surface Measurements C.

[451 Oct. 10, 1972 Hewitt Dix, Geophysics, Vol. 20, No. 1, Jan. 1955 Complex Reflection Patterns and Their Geologic Sources Frank Rieber, Geophysics, vol. 2, No. 2,

Mar. 1937 Vertical Velocities and Reflection Shooting L. W. Gardiner, Geophysics, vol. 12, No. 2, Apr. 1947 Velocity Determinations by Means of Reflection Profiles C. H, Green, Geophysics vol. 3, No. 4, Oct. 1938 Primary ExamineF-Benjamin A. Borchelt Assistant Examiner-H. A. Birmiel Attorney-William J. Scherback, Frederick E. Dumoulin, Andrew L. Gaboriault and Sidney A. Johnson [57] ABSTRACT Seismic signals from detectors forming split spreads are utilized to correct for weathering, elevation,iand the like signals from detectors forming an expanded spread. The signals of the seismic section delineated by the expanded spread have applied thereto time changes under the control of a hyperbolic generator. There are generated as a result of the sweeping across the section and lengthwise thereof of the seismic signals the generation of functions utilized to provide normal moveout corrections of greater precision or accuracy than heretofore. With the normal moveout corrections of greater accuracy applied to the signals of the seismic section, additional corrections are made for dip and thereafter for delineation of the velocity characteristics of the earth along the stratigraphic column. There is included provision not only for identification of primary reflections and multiples but also for the elimination of multiples from the signals of the seismic section. The foregoing operations are carried out in an automatic system which may be either of the analog or digital type.

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1. In seismic exploration, the method of establishing weathering corrections in the form of individual static time-corrections for the signals from each of a plurality of seismic detecting stations spaced one from the other along a traverse which comprises generating at generating stations seismic signals adjacent selected ones of said detecting stations whereby the magnitudes of said static corrections At said selected stations are known, applying said known static corrections respectively to signals generated at said selected stations, applying relative to said known corrections interpolated static corrections to the remaining signals generated at the remaining of said detecting stations, and thereafter generating at generating stations further seismic signals at spaced locations along said traverse, detecting at the location of a first group of said stations and thereafter at other locations of other groups of said stations seismic signals, said locations being selected in reference to the locations of said second-named generating stations for the production of an expanding-spread seismic-section having applied to the signals from each of said detecting stations said static corrections, and applying dynamic normal moveout corrections to the signals of each group of said detectors to correct them for geometrical spreading, adding together the signals of each said group of detecting stations to form composited signals in number equal to the number of said groups, sequentially applying to said composited signals time-corrections of differing magnitude and respectively conforming with scanning functions respectively proportional to the magnitudes of the differences between one hyperbolic function and that of a differing hyperbolic function, adding together said composited signals after application thereto of each said time-correction and separately recording the resultant summation signals for each differing time-correction applied thereto for identifying signals representative of single reflections and of multiple reflections.
 2. The method of claim 1 in which said signals representative of multiple reflections are inverted and added to said composited signals of said groups to remove therefrom signals representative of said multiple reflections and concurrently to remove their effects from the to occurrence of signals representative of said single reflections, and varying said normal moveout corrections by amounts determined by the magnitudes of said scanning functions and at times determined by the time-occurrence on said summation signals of primary reflections to establish precise conformity with the velocity distribution of subsurface formations disposed below said traverse.
 3. The method of claim 2 in which said signals of said expanded-spread record-section are re-recorded after application thereto of said modified normal moveout corrections, and adding together the signals within each of said groups to form composited signals equal in number to the number of said groups whereby multiple reflections cancel while single reflections add cumulatively.
 4. The method of claim 2 in which said signals of said expanded-spread record-section after application thereto of said modified normal moveout corrections are recorded as follows: (1) the traces forming an intermediate split-spread in the expanded-spread seismic-section are recorded without addition thereto of other traces, (2) after expiration of a time interval corresponding with the arrival time of shallow reflections there are added on a trace-by-trace basis to said centrally disposed traces signals from the detecting stations of spreads located to the right and to the left of the stations forming said split-spread, and (3) after the expiration of a time interval exceeding that during which reflections from reflecting beds of intermediate depth appear adding on a trace-by-trace basis to the sum of the preceding signals the signals from the detecting stations forming the outermost spreads of the expanded-spread seismic-section.
 5. The method of claim 4 in which linear dip-scanning corrections are applied to said last-named composited signals, separately recording the resultant composited signals with each differing linear dip-scanning correction applied thereto for establishing in terms of the magnitude of each dip-scanning correction the dip of each reflecting bed.
 6. The method of claim 5 in which said last-named composited signals are added together for production of a single composited signal in which said reflections appear in succession thereon.
 7. The method of establishing magnitudes of weathering corrections individual to each of a plurality of detecting stations along a line of substantial length and forming an expanding-spread section which comprises generating seismic signals at a plurality of said detecting stations along said line, concurrently recording signals from first one and then the remainder of groups of said detector stations, each group including a plurality of stations symmetrically located along said line with respect to a generating station to form a split-spread, recording the signals from each said split-spread, the first-arrival times at the detecting stations located centrally of each split-spread providing the known magnitudes of static weathering corrections applicable thereto, applying said static corrections to said signals detected at said centrally located stations, generating playback signals from said split-spread recordings, during the generation of said playback signals applying dynamic normal moveout corrections thereto, visually displaying said signals, applying static corrections to bring into time-alignment corresponding components of said playback signals with said components of said centrally corrected signals, recording seismic signals from said detecting stations to form an expanding spread section, and applying said static corrections to playback signals from the recorded signals of said expanded-spread section the amount of each static correction for each detecting station corresponding with the static correction applied to that detecting station as determined by said split-spread records.
 8. The method of claim 7 in which dynamic corrections are applied to said playback signals of said expanded-spread section to correct for normal moveout and recording said corrected signals to form a corrected expanded-spread record-section.
 9. In seismic exploration the method which comprises (1) generating a first seismic impulse at a first sending station, (2) at a plurality of detecting stations, two of which are located at points of known weathering and all of which are spaced one from another along a line substantial distances from said first sending station, generating a first set of signals representative of seismic waves resulting from said first seismic impulse and each including components thereof reflected upwardly from a first segment of a subsurface bed intermediate said first sending station and said detecting stations, (3) storing said first set of signals, (4) generating a second seismic impulse at a second sending station located adjacent said detecting stations, (5) at said detecting stations generating a second set of signals representative of seismic waves resulting from said second seismic impulse and each including components thereof reflected upwardly from a second segment on subsurface beds more directly under said detecting stations than said first segment, (6) introducing individual static adjustments in the two of said second set of signals generated at said two detecting stations to establish a base for weathering correction for the remainder of said detecting stations, (7) modifying said second set of signals by time-variable amounts to correct for geometrical time distortion, (8) applying individual static adjustments to the signals of said second set of signals other than said two signals for alignment of said components therein to correct the remainder of said second set of signals for weathering, and (9) introducing the same static adjustments to said first set of signals as introduced to said second set of signals to correct the said first set of signals for weathering peculiar to each of said detecting stations.
 10. In seismic exploration the method which comprises (1) generating a first set of signals representative of sEismic waves resulting from generation of a first seismic impulse at a first sending station and including components reflected upwardly from a first segment on a subsurface bed located intermediate said first sending station and arriving at detecting stations located along a line extending from said first sending station, (2) storing said first set of signals, (3) generating a second set of signals representative of seismic waves resulting from generation of a second seismic impulse at a second sending station and including components reflected upwardly from a second segment on said subsurface bed located substantially directly below said detecting stations, (4) applying individual weathering correcting static adjustments to two signals of said second set from two of said detecting stations at which weathering is known, (5) applying to said second set of signals time variable adjustments representative of differences between the travel paths of said second acoustic impulse to succeedingly deeper beds and paths extending from said detecting stations perpendicular to said second segment to produce a modified set of signals representative of the travel of said second acoustic impulse over such perpendicular paths, (6) establishing alignment in a reflection component common to said modified set of signals by applying individual static adjustments to signals of said modified set of signals other than said two signals, and (7) applying to each signal of said first set the same individual static adjustment as applied to the signal in said second set from the same detecting station to correct said first set for weathering peculiar to each said detecting station.
 11. In seismic exploration the method which comprises (1) generating a first set of signals representative of seismic waves resulting from generation of a first seismic impulse at a first sending station and including components reflected upwardly from a first segment on a subsurface bed intermediate said first sending station and arriving at detecting stations located along a line extending from said first sending station, (2) storing said first set of signals, (3) generating a second set of signals representative of seismic waves resulting from generation of a second seismic impulse at a second sending station and including components reflected upwardly from a second segment on said subsurface bed located substantially directly below said detecting stations, (4) applying individual static weathering correcting adjustments to two signals of said second set from two of said detecting stations at which surface weathering conditions are known, (5) applying to said second set of signals time-variable adjustments representative of differences between the travel paths of said second seismic impulse to succeedingly deeper beds and paths extending from said detecting stations perpendicular to said segment to produce a modified set of signals representative of the travel of said second seismic impulse over such perpendicular paths, (6) establishing alignment of a reflection component common to said modified set of signals by applying individual static adjustments to signals of said modified set of signals other than said two signals, (7) generating a modified first set of signals by reproducing each signals of said first set of signals and applying thereto the same individual static adjustment as applied to the signal in said second set from the same detecting station to correct said first set for weathering peculiar to each detecting station, and (8) recording said modified first set of signals to form an expanding-spread record section corrected for differences in weathering underlying individual detecting stations.
 12. A system of establishing individual weather corrections for each of a plurality of seismic detectors spaced one from the other along a line, comprising means including a first group of transducers for generating signals from First groups of said detectors which, in respect to sources of seismic energy applied to the earth form split-spreads whereby the weathering corrections for detectors located midway of each split-spread are known, means for adjusting the transducers corresponding with each of said detectors located midway of said split-spreads for introducing time-corrections in the signals generated thereby which correspond respectively with said known weathering corrections, display means having a plurality of input circuits, means connecting a plurality of said transducers to said input circuits of said display means and including at least two detectors for which said weathering corrections are known, means for adjusting aid transducers to introduce time-alignment of selected common components of signals from said detectors to bring said components into alignment with like components of said detectors in respect to which said weathering corrections have been made, a second set of transducers for reproducing from said detectors an expanding-spread record-section, and means operable concurrently with adjustment of said first-named transducers for correspondingly adjusting the transducers of said second set to introduce weathering corrections on a trace-by-trace basis corresponding with those applied to said first-named transducers.
 13. The system of claim 12 in which there are provided normal moveout means for introducing dynamic corrections for the signals from said transducers forming said split-spreads, to compensate for geometrical spreading, and in which said weathering corrections for all of said transducers except those for which weathering corrections are known are introduced during their relative adjustment by said normal moveout means.
 14. In seismic exploration, the method which comprises applying to seismic signals of an expanded-spread record-section dynamic corrections based upon an approximate velocity profile of formations underlying said section and representative of the differences between the travel paths of acoustic energy from spaced generating stations and a path perpendicular to a common reflecting segment, combining the signals from selected groups of traces of said record-section to form sets of seismic signals in number equal to the number of said groups, generating a plurality of sets of summation signals each of which is representative of the sum of each said set of signals displaced in time one from the other in accordance with differences between a plurality of preselected hyperbolic functions, wherein some of said summation signals include reflection components which are indicative of multiple reflections and others are indicative of single reflections, correcting to a more exact velocity profile said time corrections by modifying said dynamic time corrections based upon said approximate velocity profile by amounts related to the degree of eccentricity of said hyperbolic functions which produce cumulative addition of reflection signals, reproducing said signals of said expanding-spread record-section, and applying to said last-named signals dynamic corrections based upon said more exact velocity profile.
 15. A method of producing an improved record of seismic data which method comprises: generating signals corresponding with a seismic section composed of seismograms including multiple reflections and primary reflections reflected from common segments of subsurface reflecting horizons after travel to said segments over a plurality of paths, said primary reflections and said multiple reflections appearing across said section with time differences closely approximating hyperbolic arcs of varying eccentricities: repeatedly scanning the signals along said seismograms and across said section under the control of different hyperbolic scanning functions of respectively different eccentricities: closely approximating hyperbolic arcs to identify with reference to said scanning functions the signals representative of primary reflections; producing corrective functions in response to those of said scanning functions which produce said identification of signals representative of said primary reflections; and thereafter combining the signals of said seismograms, after normal moveout correction thereof in time-relation at least in part determined by said corrective functions.
 16. The method of claim 15 in which there is performed the additional step of establishing the relationship between vertical travel time and average velocity of the acoustic energy to each corresponding reflecting point located at successively greater depth in accordance with said corrective functions which produce identification of said signals representative of said primary reflections.
 17. The method of claim 15 in which the additional step is performed of compositing the seismograms of said seismic section which are representative of reflections from a common depth point to increase the amplitude of said signals representative of primary reflections and to attenuate signals representative of multiple reflections.
 18. The method of claim 17 in which the additional step is performed of separately and reproducibly recording said signals of increased amplitude representative of said primary reflections.
 19. The method of claim 18 in which the additional steps are performed of applying a series of different linear dip-scanning corrections to said last-named recorded signals, separately recording the resultant signals from each differing linear dip-scanning correction applied thereto for establishing in terms of the magnitude of each dip-scanning operation the dip of each reflecting horizon, and adding together said resultant signals for production of a single composited signal in which the reflections appear in succession on a single trace of a record.
 20. The method of claim 15 in which only centrally located seismograms forming said seismic section are composited to increase the amplitude of said signals representative of primary reflections and to attenuate signals representative of multiple reflections resulting from reflecting horizons at shallow depth, and at increasing depths of said reflecting horizons compositing with said centrally located seismograms additional seismograms located respectively on opposite sides of said centrally located seismograms thereby to eliminate the effect of first breaks and surface noise from the outermost groups of seismograms with resultant enhanced signals representative of reflections from the deeper reflecting horizons.
 21. The method of claim 15 in which the eccentricities of said hyperbolic scanning functions cover ranges at least as great as the range of eccentricities in the hyperbolic arcs formed by said primary reflections and by said multiple reflections.
 22. The method of claim 21 in which signals representative of multiple reflections identified by said scanning functions are inverted in phase, and adding said inverted multiple reflections in time coincidence with the appearance of the multiple reflections of said seismograms substantially to cancel from said seismograms signals representative of said multiple reflections.
 23. The method of claim 22 in which there is performed the additional step of applying the phase-inverted signals to the inverse of said hyperbolic scanning functions for generating a plurality of traces on which there appear only the phase-inverted signals representative of said identified multiple reflections.
 24. The method of claim 15 in which there are a plurality of seismic sections relating respectively to predetermined points along a traverse of the area being explored, the plurality of common segments of successively deeper reflecting horizons for each said seismic section delineating a stratigraphic column, and which comprises, after the combining of the signals following said normal moveout corrections established at least in part by said corrective functions, establishing from the time-amplitude functions of the appearance thereon of primary reflections And interval-velocity profile for each of said columns, and registering such interval-velocity profiles at spaced points along said traverse representative of the surface locations of said columns.
 25. In seismic exploration where a family of seismograms are produced each consisting of a set of signals each including components representative of seismic waves reflected from a set of subsurface reflecting points after travel to said point over paths, which paths for any one of said seismograms largely differ from the paths for any other of said seismograms, the method which comprises generating a control function dependent upon time occurrences of successively deeper reflections and an assumed velocity distribution of earth formations through which said paths extend, dynamically shifting in time components of each of said signals in dependence upon said control function to correct the time occurrence of said components for spread geometry distortion to produce corrected sets of said signals, combining signals of each of said corrected sets of signals which include reflections from the same point in said set of points to form a composite record representative of reflections traveling over all of said paths, and recording the combined signals.
 26. In seismic exploration where a family of seismograms are produced each consisting of a set of signals including reflection components representative of seismic waves reflected from a set of subsurface reflecting points after travel to said points over paths which for any one of said seismograms differ from those of other of said seismograms, the method which comprises individually modifying the time relationships between components of each of the signals in said set of signals in dependence upon an assumed velocity distribution along said paths and the geometrical relations between said paths and said reflecting points substantially to eliminate time distortion in a resultant secondary set of seismic signals, generating a control function dependent upon variations in time occurrences of successively later reflection components in said secondary set of signals to modify and make exact said assumed velocity distribution, individually modifying the time relationships between components of each of the signals in said set of signals in dependence upon said control function to eliminate time distortion in a resultant modified set of signals, and recording said modified second set of signals.
 27. The method of identifying the presence of multiples in signals from an expanded-spread record which comprises applying to said signals time-adjustments the magnitudes of which vary across the record in accordance with a plurality of hyperbolic functions of different eccentricities and through a range of hyperbolic functions whose curves have opposite concavities, adding together after application of each of said corrections the resultant signals whereby signals representing multiple reflections add together cumulatively upon application of certain of said corrections and single reflections add together cumulatively upon application of other of said corrections to said signals.
 28. In seismic exploration the method comprising generating signals corresponding with an expanding-spread seismic record-section, combining said signals with successively applied time-corrections to provide a plurality of summation signals, said successively applied time-corrections corresponding with hyperbolic sweeping functions each of varying eccentricity with respect to said signals of said record-section, and separately storing said plurality of summation signals along like space scales for producing cumulative addition of signals identifiable in terms of the eccentricity of said sweeping functions.
 29. In seismic exploration the method comprising generating signals corresponding with an expanding-spread record-section across which there appear primary reflections and multiple reflections with time differences across said section closely approxImating hyperbolic arcs of varying eccentricities, combining said signals with each of a plurality of differing time changes to provide a corresponding plurality of summation signals, a first group of said time changes including hyperbolic sweeping functions of eccentricities covering a range at least as great as the range of eccentricities in said hyperbolic arcs formed by said primary reflections and a second group of said time changes including hyperbolic sweeping functions of eccentricities covering a range at least as great as the range of eccentricities in hyperbolic arcs formed by said multiple reflections, and separately storing said plurality of summation signals respectively identifiable in terms of the eccentricities of said sweeping functions.
 30. The method of claim 29 in which said generated signals toward the end-traces of said summation signals are amplified relative to the signals representative of the intermediate traces.
 31. The method of claim 29 in which said signals of the several traces corresponding with said expanding-spread record-section are modified in amplitude to provide increasingly greater amplitudes of the signals of the traces spaced outwardly of the central traces.
 32. In seismic exploration where a family of seismograms are produced, each seismogram including multiple reflection signals and a plurality of single reflection signals representative of waves reflected from subsurface reflecting points after travel to said points over a plurality of paths, each of which for any one of said seismograms differs from the path for any other of said seismograms, the method which comprises: generating signals from each of said seismograms, applying to said generated signals a succession of dynamic adjustments, one for each said seismogram, and of magnitude to correct for normal moveout delays present in said seismograms, time-shifting said generated signals, the magnitude of the time-shifts varying across said family of seismograms in accordance with a plurality of approximate hyperbolic functions of different eccentricities, and adding together said generated signals for the production of summation signals representing (a) multiple reflections which add together cumulatively for certain of said hyperbolic functions, and (b) single reflections which add together cumulatively for other of said hyperbolic functions.
 33. The method of claim 32 in which said family of seismograms for an expanded-spread, and in which said signals of said family of seismograms are modified for establishing greater amplitudes of the signals of the seismograms spaced outwardly of the central seismograms of the expanded-spread than the amplitudes of the signals of the centrally located seismograms of said expanded-spread.
 34. The method of claim 32 in which there are recorded, for each dynamic time-adjustment resultant summation signals for establishment of the relationship between vertical travel time and average velocity of the acoustic energy to each corresponding reflecting point located at successively greater depths, and applying to said family of seismograms dynamic normal moveout corrections based upon said values of vertical travel time and of said average velocities so determined.
 35. The method of utilizing an automatic computing system to treat seismic data representative of characteristics of earth formations traversed by a stratigraphic column comprising the steps of: a. inputting to the automatic computing system a seismic section derived from the seismic data and comprised of seismograms including primary reflections reflected from common segments of subsurface reflecting horizons in the column after travel to said segments over a plurality of paths; b. repeatedly searching for signals across said section and along said seismograms under control of different hyperbolic functions to determine the presence of primary reflections; c. producing from the result of said searching steps functions which idenTify alignment of reflections with respect to the eccentricities of said hyperbolic functions; and d. utilizing said functions for producing normal moveout corrections for said seismic section.
 36. A system for use in seismic exploration wherein a seismic section is delineated by a plurality of seismograms including signals representing multiple reflections and primary reflections reflected from common segments of subsurface reflecting horizons after travel to said segments over a plurality of paths, said primary reflections and said multiple reflections appearing across said section with time differences closely approximating hyperbolic arcs of varying eccentricities, said system comprising: means for generating hyperbolic scanning functions closely approximating hyperbolic arcs of different respective eccentricities; means operable under the control of said hyperbolic scanning functions for repeatedly scanning the signals along said seismograms and across said section to identify with reference to said scanning functions the signals representative of primary reflections; means responsive to each said scanning function which identifies signals representative of primary reflections for producing a corrective function; and means for applying to the plurality of seismograms dynamic normal moveout corrections based upon the values of vertical travel time and of the average velocities, which corrections at least in part are determined by said corrective functions.
 37. The system of claim 36 in which means are provided for compositing the seismograms of said seismic section which are representative of reflections from a common depth point to increase the amplitude of said signals representative of primary reflections and to attenuate signals representative of multiple reflections.
 38. The system of claim 37 in which means are provided for separately and reproducibly recording said signals of increased amplitude representative of said primary reflections.
 39. The system of claim 38 in which means are provided for applying a series of different linear dip-scanning corrections to said last-named recorded signals, the resultant signals being separately recorded with each differing linear dip-scanning applied thereto for establishing in terms of the magnitude of each dip-scanning operation the dip of each reflecting horizon.
 40. The system of claim 36 comprising means for compositing only centrally located seismograms forming said seismic section to increase the amplitude of said signals representative of primary reflections and to attenuate signals representative of multiple reflections resulting from reflecting horizons at shallow depth, and means at increasing depths of said reflecting horizons for compositing with said centrally located seismograms additional seismograms located respectively on the opposite sides of said centally located seismograms thereby to eliminate the effect of first breaks and surface noise from the outermost groups of seismograms with resultant enhanced signals representative of reflections from the deeper reflecting horizons.
 41. A system for establishing the magnitude and sense of any error in a known velocity distribution function which may only approximate the velocity distribution function of a given stratigraphic column which comprises means for producing a first set of expanded-spread seismograms each of which includes seismic reflections from reflecting layers encountered in said column, means for applying corrections to said first set including dynamic corrections based upon said known velocity distribution function to produce a second set, means for generating error signals representative in magnitude and sense of the magnitude and direction respectively of the variations in time occurrence of successive reflections in said second set, and registering means for recording said error signals.
 42. A system for establishing an exact velocity distribution function from a set of expanded spread seismic reflection signals statically corrected both for weathering and for elevation along the expanded-spread which comprises means for establishing an approximate velocity distribution function for formations underlying said spread, means for applying to said set dynamic corrections dependent upon said approximate velocity distribution function to produce a secondary set approximately corrected for spread geometry, means for reproducing said secondary set, and means for modifying said approximate velocity distribution function at time points therealong corresponding with the time occurrence of reflection signals in said secondary set where the amounts of said corrections and the sense thereof are respectively dependent upon the magnitude and direction of variations in the time occurrence of reflection signals in said secondary set.
 43. A system for establishing an exact velocity distribution function from a set of expanded-spread seismic reflection signals statically corrected both for weathering and for elevation along the expanded-spread which comprises means for applying to said set dynamic corrections dependent upon an approximate velocity distribution function for formations underlying said spread to produce a secondary set approximately corrected for spread geometry, means for reproducing said secondary set, means for modifying said approximate velocity distribution function at time points therealong corresponding with the time occurrence of reflection signals in said secondary set where the amounts of said corrections and the sense thereof are respectively dependent upon the magnitude and direction of variations in the time occurrence of reflection signals in said secondary set, and means for registering the modified velocity distribution function.
 44. A system for establishing an exact velocity distribution function from a set of expanded-spread seismic reflection signals statically corrected both for weathering and for elevation along the expanded spread which comprises means for applying to said set dynamic corrections dependent upon an approximate velocity distribution function Delta T vs. To where Delta T is the magnitude of correction at a given record time To for formations underlying said spread to produce a secondary set approximately corrected for spread geometry, means for reproducing said secondary set, means for modifying said approximate velocity distribution function at time points therealong corresponding with the time occurrence of reflection signals in said secondary set where the amounts of said corrections and the sense thereof are respectively dependent upon the magnitude and direction of variations in the time occurrence of reflection signals in said secondary set to produce a function Delta T'' vs. To, where Delta T is defined as the exact velocity distribution function and means for producing an apparent average velocity function Va in accordance with the expression where x is the horizontal distance along said spread between sending and receiving stations for a given signal in said set.
 45. In seismic exploration, the method of generating signals corresponding with a seismic section comprised of seismograms including primary reflections reflected from common segments of subsurface reflecting horizons after travel to said segments over a plurality of paths, said primary reflections appearing across said record section with time differences closely approximating hyperbolic arcs of varying eccentricities, combining said signals with each of a plurality of differing time changes to provide a corresponding plurality of summation signals, a first group of said time changes including hyperbolic sweeping functions of eccentricities covering a range at least as great as the range of eccentricities of said hyperbolic arcs formed by said primary reflections, and separately storing said plurality of summation signals rEspectively identifiable in terms of the eccentricities of said sweeping functions.
 46. The method of claim 45 in which functions are generated from said summation signals above a predetermined amplitude, and thereafter combining the signals of said seismograms after normal moveout corrections at least in part determined by said functions.
 47. The method of claim 46 in which there is performed the additional steps of: applying a scanning function to said seismograms after correction for normal moveout for determination of direction and extent, if any, of the dipping of said reflecting horizons, and computing from the direction and extent of dipping of said horizons a velocity log of the earth corrected for dip.
 48. The method of claim 47 in which there is performed the additional step of: inverse filtering said reflections for producing a velocity log of the earth extending to said lowermost one of said segments. 